Abstract
The mechanisms of atrial fibrillation (AF) are a challenging research topic. The rotor hypothesis states that the AF is sustained by a reentrant wave that propagates around an unexcited core. Cardiac tissue heterogeneities, both structural and cellular, play an important role during fibrillatory dynamics, so that the ionic characteristics of the currents, their spatial distribution and their structural heterogeneity determine the meandering of the rotor. Several studies about rotor dynamics implement the standard diffusion equation. However, this mathematical scheme carries some limitations. It assumes the myocardium as a continuous medium, ignoring, therefore, its discrete and heterogeneous aspects. A computational model integrating both, electrical and structural properties could complement experimental and clinical results. A new mathematical model of the action potential propagation, based on complex fractional order derivatives is presented. The complex derivative order appears of considering the myocardium as discrete-scale invariant fractal. The main aim is to study the role of a myocardial, with fractal characteristics, on atrial fibrillatory dynamics. For this purpose, the degree of structural heterogeneity is described through derivatives of complex order γ = α + jβ. A set of variations for γ is tested. The real part α takes values ranging from 1.1 to 2 and the imaginary part β from 0 to 0.28. Under this scheme, the standard diffusion is recovered when α = 2 and β = 0. The effect of γ on the action potential propagation over an atrial strand is investigated. Rotors are generated in a 2D model of atrial tissue under electrical remodeling due to chronic AF. The results show that the degree of structural heterogeneity, given by γ, modulates the electrophysiological properties and the dynamics of rotor-type reentrant mechanisms. The spatial stability of the rotor and the area of its unexcited core are modulated. As the real part decreases and the imaginary part increases, simulating a higher structural heterogeneity, the vulnerable window to reentrant is increased, as the total meandering of the rotor tip. This in silico study suggests that structural heterogeneity, described by means of complex order derivatives, modulates the stability of rotors and that a wide range of rotor dynamics can be generated.
Highlights
Atrial fibrillation (AF) represents an important socio-economic burden for world health systems (Kirchhof et al, 2016)
A reduction of 9 ms is achieved by fixing α = 2 and increasing β from 0 (APD = 108 ms) to 0.28 (APD = 99 ms)
Our results suggest that structural changes reduce the action potential duration (APD) under chronic AF (CAF) conditions
Summary
Atrial fibrillation (AF) represents an important socio-economic burden for world health systems (Kirchhof et al, 2016). As the AF perdures in time, the ablation effectiveness decreases significantly (Kirchhof et al, 2016; Lim et al, 2017) During this chronic AF (CAF) scenario, the pathophysiological substrate sustains a more complex form of the arrhythmia. Recent clinical studies report high rates of success when targeting rotors as ablation sites in CAF patients (Narayan et al, 2012, 2013; Miller et al, 2017). This investigation provides evidence in favor of the rotor hypothesis, but controversy persists since some researchers were not able to replicate the results (Buch et al, 2016; Steinberg et al, 2017). A better understanding of the rotor dynamics and the effect of structural heterogeneity, could lead to deeper knowledge for determining critical ablation targets
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